We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation.
@article{1085408502,
author = {Marinucci, Domenico and Piccioni, Mauro},
title = {The empirical process on Gaussian spherical harmonics},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 1261-1288},
language = {en},
url = {http://dml.mathdoc.fr/item/1085408502}
}
Marinucci, Domenico; Piccioni, Mauro. The empirical process on Gaussian spherical harmonics. Ann. Statist., Tome 32 (2004) no. 1, pp. 1261-1288. http://gdmltest.u-ga.fr/item/1085408502/